asinus

If he used 1/6 of his salary to pay the household bills, how much was his total salary?

Hello Guest!

What is used in the household accounts in the ratio 3: 2 please?

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What is the largest value of k...

Hello Guest!

\( 6x - x^2 = -4x + k\\ x^2-10x+k=0\\ x=5\pm \sqrt{25-k}\\ \color{blue}k\leq 25\)

The largest possible value for k is 25.

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Find angle x, in degrees.

Hello Guest!

\(7y+5y=180^o\\ y=15^o\\ x=180^o-(5+3)\cdot 15^o\)

\(x=60^o\)

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Find all positive integers n such that n^2 is divisible by n - 12.

Hello Guest!

\(\{n,N\} \subset \mathbb N\\ N=\frac{n^2}{n-1}\)

   n  |   36   48   60   84   156 

   N |   54   64   75   98   169

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 Wie viel prozent?

Hallo Gast!

\(350:42=100\%:p\\ p=\frac{42\cdot100\%}{350}=\color{blue}12\%\)

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Ich meine, wenn der Vorrat vollständig aufgebraucht ist, gibt es keine Verbrauchsmöglichkeiten.  Oder, vielleicht sind danach 2021 Nüsse neu gesammelt worden. Das müsste dann vorausgesetzt werden.

Gerade in Mathe muss eine Aufgabe korrekt formuliert sein. Das gilt vor allem kurz vor dem Abi. SCNR

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What is the minimal possible value of |a-b|?

Hello Guest!

\(ab-6a+5b=15\\ b(a+5)-6a=15\\ b=\frac{15+6a}{5+a}\)

\({\color{blue}5}=\dfrac{15+6\cdot {\color{blue}10}}{5+{\color{blue}10}}\)

The minimal possible value of |a-b| is 5.

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What is x + y?

Hello Guest!

\(3x + y + xy = 115\\ y(1+x)+3x=115\\ y=\frac{115-3x}{1+x}\)

If x = 1 then is y = 56.

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Find 1/(a - 1) + 1/(b - 1).

Hello Guest!

\(2x^2 - 9x + 2 = 0\\ x\in \{a,b\}\\ x\in \{(\frac{9}{4}+\frac{\sqrt{65}}{4} ),(\frac{9}{4}-\frac{\sqrt{65}}{4})\}\)

\(\color{blue}\frac{1}{a-1}+\frac{1}{b-1}\\ =\dfrac{1}{\frac{9}{4}+\frac{\sqrt{65}}{4}-1}+\dfrac{1}{\frac{9}{4}-\frac{\sqrt{65}}{4}-1}\\ \color{blue} =-1\)

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Danke!

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